The K2 Galactic Archaeology Program: Overview, target selection, and survey properties

ABSTRACT

1 INTRODUCTION

The use of asteroseismology to inform studies of the Milky Way was proposed over a decade ago (Miglio et al. 2009), when it became possible for the first time to detect oscillations in hundreds, even thousands, of distant stars using continuous high-cadence, photometric data from space-based missions; particularly from CoRoT and Kepler (e.g. De Ridder et al. 2009; Stello et al. 2013). However, these early missions were far from ideal for studying the Galaxy as a whole, and indeed were never designed with this in mind (Sharma et al. 2016, 2017). The main reasons were the limited sky coverage and the lack of a well-defined, and hence reproducible, target selection function. A reproducible selection function is fundamental if we are to make meaningful comparisons between observed and synthetic/modelled stellar populations (Sharma et al. 2011). Such studies play an important role in making robust inferences about the Galactic stellar populations.

A decade ago, the primary NASA Kepler mission targeted a single field in the Cygnus and Lyra constellations for four years. In 2014, the compromised satellite was then re-purposed for a new mission to stare for |$\sim 80\,$| d at a time in different directions along the ecliptic (Fig. 1); the so-called ‘K2 mission’. K2 was now able to probe stellar populations in many directions, covering much more of the Galaxy than achieved in earlier missions. This included the halo, the bulge, the thin and thick discs, and at vastly different Galactic radii and heights above and below the plane. To take advantage of this opportunity, the K2 Galactic Archaeology Programme (K2GAP) was formed around an international collaboration with the aim of detecting oscillations in thousands of red giants along the ecliptic (Stello et al. 2015).

Figure 1.

Footprint of the different K2 campaigns in Galactic coordinates. Campaigns C0, C9, C18, and C19, are not suitable for selection-function-based studies and are shown in green. The first three of these do not follow a well defined colour–magnitude selection while C19 has very few seismic detections.

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The primary goal was to establish robust stellar ages for the major Galactic stellar components (Rendle et al. 2019; Sharma et al. 2019), and to significantly improve on what was possible with ESA’s Gaia and ground-based spectroscopic survey data alone (Bland-Hawthorn et al. 2019). This was achieved by devising a well-documented, reproducible target selection to eliminate the limitations of previous space-based seismic observations, and to maximize the synergy with Galactic spectroscopic surveys. In total, K2 provided 18 full-length observing campaigns before the fuel ran out and the spacecraft was retired by the end of 2018. The K2GAP survey has already published a ‘proof of concept’ study (Stello et al. 2015) along with a succession of well-tested data products. These are Data Release 1 (DR1) containing seismic results from campaign 1 (C1) (Stello et al. 2017), Data Release 2 (DR2) containing seismic results for C3, C6, and C7 (Zinn et al. 2020), and the final Data Release 3 (DR3) with results from all campaigns in one homogeneous catalogue (Zinn et al. 2022). In addition, science results were published by Rendle et al. (2019), Sharma et al. (2019, 2021b), and Zinn et al. (2022).

The overarching vision for the K2GAP seismic data was always that it should be combined with complementary data from the many other stellar surveys that emerged in the same decade. In recognition of K2GAP’s potential, several large ground-based, spectroscopic surveys have targeted K2GAP fields. The surveys with the largest K2GAP overlap are APOGEE (Majewski et al. 2017), K2-HERMES (Sharma et al. 2018), and LAMOST (Wang et al. 2020, 2021; Zong et al. 2020). This synergy has proven to be very effective in determining improved stellar ages for thousands of giant stars, which in turn has helped us to better understand the formation and evolution of the Milky Way (Sharma, Hayden & Bland-Hawthorn 2021a; Sharma et al. 2021b; Sharma et al. 2022).

The motivation of this paper is to help the Galactic archaeology community to pursue scientific investigations of the largest legacy data set from the K2 mission. For this, we provide a detailed explanation of the selection of the K2GAP targets and release software to implement it. We compare the observed data with predictions of Galactic models by taking the selection function into account and highlight the strength and weaknesses of both the data and the model. We provide both the observed and simulated data as a way to facilitate the future use of the K2GAP data by the community. The paper is organized as follows. In Section 2, we report the target selection for each K2 campaign in detail. Next in Section 3, we discuss detection completeness of the asteroseismic parameters ν_max and Δν for the oscillating giants. In Section 4, we proceed to make a detailed comparison of the observed distribution of stars in three quantities (ν_max, V_JK, and κ_M) with that of selection-matched mock catalogues. In Section 5, we discuss the implications of our results for asteroseismic relations and Galactic archaeology (Freeman & Bland-Hawthorn 2002). Finally, in Section 6 we summarize and present our main conclusions.

2 TARGET SELECTION

2.1 Overview of selection strategy

Our target selection strategy was designed to be easily reproducible, which aids the study of ensembles rather than individual stars. This is especially important for Galactic archaeology where we need to fit Galactic models to the observational data by taking the target selection into account (Sharma et al. 2014), but is also useful for exoplanet population studies.

A necessary first step for selecting targets is to have an input catalogue that has reliable photometry, covers all regions of the sky that we are interested in, and systematics, if any, that are well understood. With this in mind, we adopt the 2MASS (Skrutskie et al. 2006) all-sky catalogue because of its robust photometry and completeness in the magnitude range we are targeting (9 < V_JK < 16). A colour limit of (J − K_s) > 0.5 was adopted throughout the survey. This was designed to focus on red giants; our primary asteroseismic targets. Since Gaia DR1 (Sep 2016), we have parallaxes for most 2MASS stars, which can be used to select giants, but they were not available when the K2GAP targets were selected. It can be seen in Fig. 2 that most of the stars with detectable oscillations from Zinn et al. (2022) (SYD pipeline) have (J − K_s) > 0.5 and |$M_{K_s}\lt 1$|⁠. Stars with (J − K_s) < 0.5 are typically dwarfs (⁠|$M_{K_s}\gt 1$|⁠) that have oscillation frequencies that are too large to be detected by the 30-min cadence of the K2GAP data. A colour limit of (J − K_s) > 0.5 excludes some giants, such as the blue extension of the red clump stars (the so-called horizontal branch), which is predominantly metal-poor and are rare.

Figure 2.

(a) Colour and absolute magnitude distribution of all stars observed by K2 in 30 min cadence that have a Gaia EDR3 parallax. The absolute magnitude is estimated using Gaia EDR3 parallax. The vertical line J − K_s = 0.5 marks the K2GAP colour selection. The number of stars in each bin is indicated by the colour bar. (b) The subset of stars with asteroseismic detection of ν_max (SYD pipeline). Most of the stars with ν_max detections have J − K_s > 0.5. Stars with ν_max detected and |$M_{K_s}\gt 1$| have either incorrect ν_max or parallax.

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Although reduced proper motions have been used to separate dwarfs from giants in the past (Gould & Morgan 2003; Huber et al. 2016), we avoided it for multiple reasons. First, it introduces a kinematic bias, which is undesirable for Galactic archaeology. Secondly, the pre-Gaia proper motions available (UCAC) at the time of the K2GAP selection, had significant uncertainties. Finally, the dwarfs that we were not interested in were desirable for exoplanet studies; and a simple selection function would also benefit those. In summary, the simplest colour-based selection criteria was found to be the best suited for both Galactic archaeology and exoplanet population studies.

A bright magnitude limit of V_JK > 9 (H > 7 for C1, C2, and C3) was adopted. However, the faint limit was different for each campaign, with the typical limit being V_JK = 15. The limit for each campaign was determined by weighing the potential scientific return versus the drop in yield of oscillating giants when going towards fainter magnitudes. The drop in yield of oscillating giants when going fainter is due to a couple of reasons. First, in the Galaxy the overall fraction of stars that are giants for a given apparent magnitude drops as we go to fainter magnitudes. This is shown in Fig. 3. Secondly, fainter stars have lower signal-to-noise ratio (SNR), which hinders our ability to detect the oscillations. Based on simulations the incompleteness for the K2 observations was predicted to set in at around V_JK = 14; see Section 4.2 for more details. This prompted us to not propose targets in general that were too faint.

Figure 3.

The fraction of stars proposed by K2GAP that are giants as a function of apparent magnitude V_JK for different K2 campaigns. The stars satisfy the selection function given in Table 1. For this plot, giants were identified based on their absolute magnitude being |$-3.7\lt M_{K_s}\lt 1$|⁠. |$M_{K_s}$| was estimated using the Gaia parallaxes.

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2.2 Field of view

To facilitate like-for-like comparisons between model predictions and observations of the K2GAP stellar populations, we provide here details on the field of view. The K2 field of view is 115.64 deg² comprising a mosaic of 21 CCD modules, of which 2 were defunct, each made up of two 1024×2200 pixel CCDs (3.98 arcsec pixel scale) with slight gaps between the two CCDs and between the 21 modules (see Fig. 4). Although the actual area of a module is 5.507 deg², the proposed stars were confined to 5.482 deg², most likely due to a CCD-edge buffer of a few pixels introduced by the python package K2FOV (Mullally, Barclay & Barentsen 2016),¹ which we used to select the targets. For certain campaigns with high target density, we proposed stars in 1 degree circles located at the centre of selected CCD modules, to make the spectroscopic followup easier (see Fig. 5). Such a circle has a photosensitive area of 2.961 deg² (94.251 per cent of the circle’s area).

Figure 4.

Field of view of a typical K2 campaign. Shown here is campaign C1. The solid lines outline the 42 CCDs arranged in 21 modules. The defunct modules are shown in red. The green circle shows the 1 degree radius field of view of the HERMES spectrograph. Note, the module numbers defined by us is similar but not the same as the official module numbers; our numbering starts from 0 and does not count the four corners and the two defunct modules.

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Figure 5.

Distribution of K2GAP stars observed by K2 in campaigns where stars were selected to lie in one degree radius circles. Each campaign has 19 one degree circles, numbered 0 to 18, located at the centres of each CCD module (excluding the two broken CCD modules). The observed stars are denoted by black dots and the field of view is outlined.

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2.3 Peculiarities of certain campaigns

Due to a late change in roll angle for C3, the actual field of view was slightly shifted compared to the one provided by the K2Fov software before observations. This meant that some of the proposed targets were unobservable. Later, the permanent failure of one of the CCD modules (marked as 1 in Fig. 4) occurring during C10 observations resulted in selected stars falling on that module being observed for only part of C10 and not observed at all for C11, C12, and C13 as the target selection for those campaigns had already been locked in.

Campaigns C0, C9, C18, and C19 were all unique and they all turned out in the end to deliver few seismic detections. C0 was conducted as a full-length engineering test to prove the viability of the K2 mission and to fine tune the observational setup, such as pointing and choice of aperture size. C9 was dedicated for gravitational microlensing studies, hence no community targets were sought. C18 and C19 both turned out to be of relatively short duration. C18 observations were terminated after 50 d due to low fuel. About 3000 K2GAP targets were observed but all of them were found to be serendipitous selections (meaning not chosen from the K2GAP target list, but from other observing programmes), hence, their selection function is not known. C19 observations only lasted 30 d before the spacecraft ran out of fuel. This campaign also suffered from erratic pointing. Other than this, C11 also had some role angle error and had a shorter observing duration.

2.4 The selection function of the observed targets

The selection function of the targets observed by K2GAP is given in Table 1 (rightmost column). It is simply a function of 2MASS colours J, H, K_s and angular positions RA and Dec and is easily reproducible. We provide a python code that implements this function (see the section on data availability). It is colour–magnitude limited with limits varying from campaign to campaign and with circular pointing identifier c, (see Fig. 5). We now describe how targets were proposed and how we arrive at this selection function. A user interested in just working with a reproducible selection function does not need to worry about these details. However, for legacy purposes and for someone interested in understanding the full sample, it is important to present these details here.

For K2, targets were allocated via the Guest Observer programme in which various teams participated and competed against each other. Each team was asked to submit a proposal along with a ranked list of proposed targets. The rank, up to which the targets were finally selected for observation, was decided by the NASA mission office and was not disclosed. Only the final list of all selected K2 targets to be observed (across all proposals) was released. We begin by describing the procedure used to prepare the proposed K2GAP target list for each campaign. Next, we discuss the method adopted to figure out the rank upto which targets were selected from our programme. Finally, using this rank we derived the final selection function of the observed K2GAP targets, which is presented in Table 1.

Separate target lists were created for each campaign. Stars were selected to have good quality photometry as defined in Table A1. Targets in each list were sorted based on priority. A list of various priority classes and their order is given in Table B1, for further details see Appendix  B. In short, top priority was given to stars that were known to be giants, e.g. from spectroscopy. This was followed by the main sample which was selected based on photometric colour and magnitude and was sorted by magnitude. In general, stars were proposed over the entire field of view except for the dense fields (see Section 2.2). In those cases the stars belonging to the same CCD module were grouped together. The CCD modules were typically sorted based on distance from the campaign boresight centre, because stars close to the centre would show less pointing drift. The top priority targets, known to be giants prior to observations, do not follow a well-defined colour magnitude selection because they were collated from various surveys. The primary focus of our study is the main colour magnitude limited sample. We now describe the procedure to determine the effective selection function for them.

Because the final target list prepared by NASA and uploaded to the spacecraft for observation contained targets from different proposals, some of our proposed targets were serendipitous selections; their selection was based on other proposals and they just happened to also be on our target list. The serendipitous targets therefore do not follow our proposed rank order. Guided by Fig. 6 we devised a procedure to exclude these targets. Fig. 6 shows the average fraction of stars selected from our list as a function of our proposed rank order (row number of the submitted table). We see that the fraction is high and almost constant for small rank orders, but it abruptly falls to a low value for a particular rank order and remains low thereafter. The sharp fall in fraction marks the special rank order up to which the sample selection is complete but beyond which there are serendipitous targets. Identifying the special rank order up to which the sample selection is complete is a change point detection problem and for this we propose and use a new algorithm.

Figure 6.

Fraction of stars observed by K2 as a function of rank order (row number in the list of targets proposed by K2GAP). The sharp fall in fraction marks the rank order up to which the sample is complete. For most campaigns, the completeness is typically high, greater than 0.97. C3 and C12 have slightly lower completeness, 0.85 and 0.91 respectively. For C3 the completeness is low due to a roll angle error, while for C12 it is due to extra targets proposed in the broken CCD module. C13 also has slightly lower completeness due to extra targets proposed in the broken CCD module. C17 shows a two-step fall in the fraction, the cause of which is not clear.

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Using the above procedure, a total of 110 791 K2GAP stars were found to be free of serendipitous targets, which we refer to as our K2GAP complete sample (column 4 of Table 1). This is 25 per cent of the total number of stars observed by K2. From the K2GAP complete sample we identify the 101 419 stars that are colour magnitude complete (column 5 of Table 1) following the selection function listed in column 8 of Table 1. The fraction of stars satisfying the selection function that are observed is given in column 6. Typically the fraction is quite high with the average being 0.974, the exception being C2 and C3. For C3 the fraction is low due to the roll angle error mentioned in Section 2.3. For C2 the fraction is low due to the fact that stars were listed in random order unlike for other campaigns where they were sorted by magnitude.

3 OVERVIEW AND PROPERTIES OF ASTEROSEISMIC OBSERVATIONS

In this section, we provide an overview of the asteroseismic data that we use in this paper and discuss some of the properties of our sample. We begin by describing the source of our adopted asteroseismic parameters. Next, we discuss the spatial distribution of the seismic sample in the Galaxy. This is followed by a discussion of the completeness of the ν_max and Δν detections, which is useful for Section 4 where we compare the asteroseismic observations with theoretical predictions.

3.1 Asteroseismic parameters

In this paper, we use two seismic quantities: the frequency of maximum oscillation power, ν_max, and the frequency separation between overtone oscillation modes, Δν. The values we use were the so-called SYD results that are also adopted by Reyes et al. (2022) and the K2GAP DR3 catalogue (Zinn et al. 2022). We used the associate probabilities |$p_{\nu _{\rm max}}$|⁠, based on Hon, Stello & Zinn (2018b) and p_Δν, based on Reyes et al. (2022) that denote the reliability of ν_max and Δν measurements. A target with p_Δν > 0.5 was assumed to have a valid Δν. A target with |$p_{\nu _{\rm max}}\gt 0.5$| was assumed to have a valid ν_max. However, given that a Δν measurement is harder than ν_max. A small percentage of stars that had |$p_{\nu _{\rm max}}\lt 0.5$| but p_Δν > 0.5 were also deemed to have valid ν_max. In this sense our definition of valid ν_max differs from Zinn et al. (2022) who simply used |$p_{\nu _{\rm max}}\gt 0.95$|⁠. After applying these definitions, a total of 30 923 targets had a valid ν_max and of these, a total of 20 708 targets had a valid Δν. Note, some stars were observed in multiple campaigns, which means there can be multiple targets (and hence results) that correspond to the same star. To be consistent with the use of SYD results for K2, we also use the SYD results (Stello et al. 2013) when comparing with Kepler, which had a total of 12 919 targets with valid ν_max and Δν.

3.2 Spatial distribution of oscillating giants

One of the main advantages of the K2 mission over Kepler is its wider coverage of the Galaxy. This can be seen in Fig. 7, which shows the spatial distribution of oscillating giants in the Galaxy. The K2 giants span a wide region in the (R, z) plane, while Kepler giants were confined to a small range around R = R_⊙. This is specially useful for studying the formation and evolution of the Galaxy. Away from the plane the radial coverage in R extends all the way from 2 to 14 kpc (Fig. 7b, blue curve). However, close to the plane the radial extent is quite limited (Fig. 7a, |$z\sim 0\,$| kpc). In the heliocentric (x, y) projection the giants can be seen in all four quadrants, but there are more of them in the lower half defined by y_helio < 0 (Fig. 7c). Although the giants extend up to a distance of about 6 kpc from the Sun, most of the stars are within a distance of about 2.5 kpc (Fig. 7d, green curve).

Figure 7.

The spatial distribution of oscillating giants using parallax information from Gaia. Panels (a) and (b) show the distribution in Galactocentric cylindrical coordinates R and z. Away from the plane the radial coverage in R extends all the way from 2 to 14 kpc. However, close to the plane the radial extent is quite limited. Panels (c) and (d) show the distribution in heliocentric Cartesian coordinates x_helio and y_helio and distance d.

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3.3 Probability to detect ν_max

For bright stars the K2 mission is expected to detect oscillations in stars with 10 ≲ ν_max/|$\mu$|Hz ≲ 270 (Stello et al. 2015). The lower ν_max limit is due to the duration of the observations and the upper limit is due to the 30 min cadence of the data. The absolute magnitude, for example |$M_{K_s}$|⁠, increases with increasing ν_max. Hence, stars with ν_max measurements should be confined to a range in |$M_{K_s}$|⁠. This suggests that |$M_{K_s}$| can be used to estimate the overall detection probability and this can be seen in Fig. 8, where we plot the ratio of stars with ν_max measurement to the number of observed stars as function of |$M_{K_s}$|⁠. The probability in the range |$-2.5\lt M_{K_s}\lt 0$| is approximately constant, with expected falloffs at either end due to the abovementioned observational limitations. The average probability in the range |$-2.5\lt M_{K_s}\lt 0$| was found to be 0.86 for K2 and 0.89 for Kepler; representing the overall probability to detect ν_max. The slightly higher probability for Kepler is most likely due to a generally higher SNR resulting from light curves being about 12 times longer. The longer Kepler light curves, also explains why the detection probability zone extends to lower values of |$M_{K_s}$| (−3) compared to K2 (−2.5). For K2, we restrict our analysis to bright stars, 10 < V_JK < 13. The faint limit was set because fainter stars have lower SNR, which progressively makes it harder to detect ν_max, specially for stars with high ν_max, which have lower oscillation amplitudes. The bright limit on V_JK was set to avoid overly saturated stars. Changing this limit to include even brighter stars was found to have no effect on the detection probability profile shown in Fig. 8.

Figure 8.

The probability of detecting ν_max (SYD pipeline from Zinn et al. 2022) as a function of absolute magnitude |$M_{K_s}$|⁠. The probability is measured as the ratio of stars with ν_max detections to the number of stars observed in each bin of |$M_{K_s}$|⁠. The average probability in the range |$-2.5\lt M_{K_s}\lt 0$| is 0.86 for K2 and 0.89 for Kepler.

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3.4 Probability to detect Δν for a given ν_max

In Fig. 9 we show the probability of detecting Δν given a ν_max detection, with each campaign shown separately. The probability is computed as the fraction of stars with ν_max detection that also have a Δν detection. The fraction shows an undulating behaviour with two peaks, which arise from a global smooth hill shape that peaks at |$\nu _{\rm max}\sim 60\, \mu$|Hz and a local dip near ν_max of 30 |$\mu$|Hz of about 40 per cent. For the global shape, the drop towards lower and higher ν_max is analogous to what we saw for ν_max detections discussed in the previous section. The dip at |$\nu _{\rm max} \sim 30\, \mu$|Hz corresponds to the location of the red clump (RC) stars. It shows that Δν is generally harder to detect in clump stars. This is in agreement with findings of Mosser et al. (2019) who show that the autocorrelation function for RC stars is about 60 per cent lower as compared to RGB stars. The asteroseismic completeness for other pipeline results and as a function of mass and radius is considered in Zinn et al. (2022).

Figure 9.

Fraction of stars with ν_max (SYD pipeline from Zinn et al. 2022) detections that also have Δν detections.

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4 COMPARING ASTEROSEISMIC OBSERVATIONS WITH GALACTIC MODEL PREDICTIONS

One of the main aims of the K2GAP is to study the formation and evolution of the Milky Way. An important step in this process is to compare the observed asteroseismic data with the predictions of a current state-of-the-art Galactic model. This will help identify any major issues that need to be addressed before fine tuning the model. Each K2 campaign was unique with characteristics such as the light-curve duration, the pointing accuracy, and the crowding varying from campaign to campaign. Hence, it is important to highlight if the data from any campaigns are in some way problematic. For example, if observations agree with model predictions in some campaigns but not in others having similar (R, z) Galactic location, that is strong evidence for the data being problematic for those campaigns. Having described the selection function and detection completeness we now proceed to performing this model comparison.

We begin by creating a synthetic catalogue of stars in accordance with a Galactic model that satisfy the same selection function as the observed data, which is available for download, see the section on data availability. Next, we compare the model-predicted and observed distributions of various stellar properties, such as apparent magnitude and asteroseismic quantities (V_JK, ν_max, and κ_M); the latter being a seismic mass proxy that is a combination of ν_max and Δν.

4.1 Creation of the synthetic catalogue

To sample data from a prescribed Galactic model we use the galaxia² code (Sharma et al. 2011). It uses a Galactic model that is initially based on the Besançon model by Robin et al. (2003) but with some modifications. The model was updated in Sharma et al. (2019). The most significant change was the shift in mean effective metallicity of the thick disc from −0.78 to −0.162. This model with a metal rich thick disc is hereafter referred to as Galaxia (MR), while the default model from (Sharma et al. 2011) is referred to as Galaxia (MP). Through out the paper, unless explicitly mentioned, we use the model Galaxia (MR).

The main steps in creating the synthetic catalogue are as follows. Using galaxia, we create magnitude limited samples with J < 15 for each campaign over a circular area of 8 deg radius. The stars are then filtered in accordance with the selection function on colour, magnitude, and angular coordinates as described in Table 1. We provide a python function to do this (the section on data availability). Next, the synthetic stars are sub-sampled (without replacement) to match the total number of observed stars in each campaign that follow the selection function (column 5 in Table 1). In reality, to reduce Poisson noise we oversample the synthetic stars by a factor of 10 and reduce the weight of each star by a factor of 10, such that the sum of weights is equal to the total number of observed stars. For reference purposes we also show results for the Kepler mission. The selection function that we adopt for Kepler is given by equations (2) and (3) of Sharma et al. (2019). Full details to reproduce the Kepler selection function can be found in Sharma et al. (2016).

To model the seismic detection probability we follow the scheme presented by Chaplin et al. (2011) and Campante et al. (2016), see also Mosser et al. (2019). The exact procedure that was adopted is given in Section 3.4 of Sharma et al. (2019). In short, the oscillation amplitude was estimated based on stellar luminosity, mass, and temperature. The apparent magnitude was used to compute the instrumental photon-limited noise in the power spectrum, which when combined with granulation noise gave the total noise. The mean oscillation power and the total noise were then used to derive the probability of detecting oscillations (with less than 1 per cent possibility of false alarm). The synthetic stars with a detection probability greater than 0.9 were assumed to show detectable oscillations.

4.2 The distribution of stars in the (ν_max, V_JK) plane

Fig. 10 shows the distribution of observed stars in the (V_JK, ν_max) plane for different K2 campaigns (first and third columns). Results from Kepler (panel (ag)) and the combination of all K2 campaigns (panel (ai)) are also shown. The heat maps in the second and fourth columns show the number ratio of observed to model-predicted giants. It can be see that ν_max can be measured for stars as faint as V_JK = 16. However, the efficiency seems to decrease beyond V_JK = 16 (dark region in Figs 10 aj). It can be seen that in K2 there is a lack of observed stars in the upper right-hand corner of Figs 10 ai) (beyond the red dashed line). This is in agreement with predictions shown in Figs 10 aj), where the white colour signifies that the number of predicted stars is zero. This detection threshold arises because of too low oscillation amplitude (high ν_max) and too high noise (faint stars) towards this corner of the plot.

Figure 10.

Distribution of observed (the first and the third columns) stars in the (ν_max, V_JK) plane for different K2 campaigns. The results for Kepler is shown in panel (ag), while the combined results from all K2 campaigns (except C11) is shown in (ai). The panels in the second and the fourth columns plot the ratio of observed to model-predicted oscillating giants in each bin, with the average recovery rate shown in the top right of each panel. The predictions are based on simulations using galaxia. The dashed line represents the equation ν_max = −60(V_JK − 17) and is designed to roughly mark the boundary above which we cannot detect oscillations due to too low SNR (the upper right-hand region).

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The ratio of observed to model-predicted number of stars varies from campaign to campaign, and is typically between 0.66 and 0.89. When averaged over all campaigns the ratio is 0.78. We found that for stars with J − K_s > 0.5 the model overpredicts the number of giants (stars with |$M_{K_s}\lt 2$|⁠) compared to dwarfs by 7.5 per cent. If we factor that in, the ratio of observed to model-predicted giants becomes 0.84, which is very close to the fraction 0.86 which we expect based on observational limitations (Fig. 8). This is a good verification of the theoretical calculations of Chaplin et al. (2011) and Campante et al. (2016), (see also Mosser et al. 2019) that were used to estimate the seismic detection probability. The fact that the Galactic model overpredicts the number of giants needs further investigation. It could be due to the turnoff stars being bluer in the model, and hence getting excluded in our J − K_s > 0.5 cut used to select the stars.

Campaign C11 has unusually low numbers of stars with detected oscillations compared to the model prediction, with a ratio of 0.3. This could be related to the data quality, which is doubtful for a couple of reasons. First, due to an error in the initial roll angle, a correction was applied 23 d into the campaign and as a result the campaign was split into two segments. Secondly, C11, which was pointing towards the Galactic bulge, has the highest stellar density amongst all the campaigns analysed here. Due to the high stellar density the pipelines used for extracting light curves as well as for the subsequent asteroseismic analysis are most likely operating outside their nominal design range. This can severely hamper the quality of the derived asteroseismic parameters. In the following two sections, we will look at the distributions shown in Fig. 10 collapsed on to either axis.

4.3 The distribution of apparent magnitude

In Fig. 11 we show the distribution of apparent magnitude V_JK of the giants with ν_max detections. The model predictions (orange curve) are within the 16 and 84 percentile region of the observed distribution (blue shaded zone). This good match is primarily a reflection of the fact that the model correctly reproduces the number of giants as a function of magnitude. A good match in V_JK is in some sense a necessary condition before we embark on a more detailed comparison of model predictions with observations. The number of observed and model-predicted giants is listed on each panel. It can be seen that the model overpredicts the number of oscillating giants, which we discuss in more detail later on.

Figure 11.

Magnitude distribution of observed oscillating giants from K2 along with predictions from galaxia (model MR). The number of stars with ν_max detections in the observed sample and those predicted by the model are also listed in each panel. The shaded region denotes the 16 and 84 percentile Poisson uncertainty around the observed data.

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4.4 The distribution of ν_max

In Fig. 12 we now show the observed distribution of ν_max alongside the model predictions. The distribution shows a peak at around ν_max of 30.5 |$\mu$|Hz, corresponding to the RC stars. For K2, the peak of observed stars is significantly shallower compared to the prediction. This could be due to the uncertainty in ν_max being underestimated in the model or because the model is inaccurate. It could also be due to RC stars preferentially ‘escaping detection’. For K2, the observed peak is systematically shifted to lower ν_max compared to the predictions, except for C4 and C13. Interestingly, both C4 and C13 point towards the anticentre direction suggesting the model requires some changes.

Figure 12.

The probability distribution of ν_max for observed and model-predicted oscillating giants. The shaded region denotes the 16 and 84 percentile Poisson uncertainty around the observed data. The black dashed line, ν_max = 30.5 |$\mu$|Hz, shows the approximate location of the peak in the distribution of the model-predicted stars. The peak corresponds to the location of the RC giants. Panel (q) shows the same distributions for Kepler. Panel (r) shows the combined data from all K2 campaigns. The observed peak is systematically lower compared to the predictions, except for C4 and C13, which point towards the anticentre direction.

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4.5 The distribution of stars in the (ν_max, κ_M) plane

Fig. 13 shows the (ν_max, κ_M) distribution for the K2GAP stars (top row) and for the Kepler sample (third row). The model predictions for K2 and Kepler are shown in the second and fourth rows, respectively. The distributions of RC (middle column) and RGB (right-hand column) stars are also shown separately. The RGB stars are distributed over a wide range of ν_max and κ_M. However, RC stars form a diagonal sequence, with most of them lying in a narrow region marked by the two solid curves. These are curves designed by Sharma et al. (2019) to approximately segregate the RC from the RGB. Here, they aid the eye when comparing the distributions in the different panels. The sharp right edge in the RC distribution is very clear. The overdensity in the RGB distribution is due to the RGB-bump stars, and it partly overlaps with the location of the majority of the RC stars. The distributions for K2 and Kepler are very similar. However, the RC sequence is slightly sharper for Kepler, due to more precise ν_max and κ_M. Overall, the model predictions match well with the observed distributions. A comparison of panel (b) with other panels in the middle column shows that K2 has a significant number of stars to the right of the rightmost solid curve, which is neither predicted by the model (Fig. 13e) nor it is present in the Kepler data (Fig. 13h). This suggests that in K2 some RGB stars are misclassified as RC stars, which is not unexpected given the K2 observations are relatively short making the seismic RC/RGB distinction more uncertain (Hon, Stello & Yu 2018a). The RC stars with high ν_max and high κ_M are the secondary clump stars (Girardi 1999). In Kepler we do see these stars all the way till 100 |$\mu$|Hz as predicted by the models (Figs 13h, k). However, the K2 data seems to have relatively fewer of them (Figs 13b, e). Interestingly, the model-predicted sequence at ν_max below 20 |$\mu$|Hz (stars at the end of helium core burning; the so-called AGB clump stars seen in Figs 13e, k), are not seen in the data. Finally, in the models, the location of the RGB-bump is offset with respect to that in observations, with the model’s location being shifted to lower ν_max, which is a known problem of contemporary stellar evolution models (Silva Aguirre et al. 2020).

Figure 13.

Distribution of stars in the (κ_M, ν_max) plane. Panels (a,b,c) show result for K2 stars. Panels (d,e,f) show theoretical predictions for K2. Panels (g,h,i) show results for Kepler stars. Panels (j,k,l) show theoretical predictions for Kepler. Left-hand columns show the results for all stars, the middle columns show the results for RC stars while the right-hand columns show the results for RGB stars. The solid lines (two curves and a horizontal line) are drawn to aid the eye when comparing the distributions in the different panels. The two curves are from Sharma et al. (2019), which were designed to roughly identify the RC stars.

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4.6 The distribution of stars in κ_M

In this section, we explore the distribution of κ_M and compare them with the predictions of the Galactic models. The distribution of κ_M is one of the most sensitive tests of the Galactic models, because κ_M is related to mass, which in turn is related to age and metallicity of a star. Hence, the distribution of κ_M probes the age and metallicity distribution of stars in the Galaxy.

In Fig. 14 we show the distribution of κ_M for the 16 K2 campaigns and Kepler. Distributions for high-luminosity RGB (hRGB), RC, and low-luminosity RGB (lRGB) stars are shown separately. This was done because the probability to detect Δν varies with stellar type for K2 (Fig. 9), suggesting systematic effects for different stellar types. The stars were split into these categories based on their location in the (ν_max, κ_M) plane (see Fig. 13); hRGB (left of leftmost solid curve), RC (between the two solid curves), and lRGB (right of rightmost solid curve). A similar analysis was initially done by Sharma et al. (2019) using data from only 4 K2 campaigns. Our results in Fig. 14 with 16 K2 campaigns confirm the findings of Sharma et al. (2019) but with better statistical accuracy.

Figure 14.

The distribution of κ_M for different K2 campaigns and Kepler. Distributions for three different stellar classes, high-luminosity RGB, RC, and low luminosity RGB stars are shown separately. The classification was done using the two solid curves in Fig. 13. In each panel, the number of observed and model-predicted stars are listed on the right-hand side. The bottom row shows the distributions for Kepler.

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The observed κ_M distribution of the lRGB stars is in good agreement with the predictions. For hRGB stars, due to the low number of observed stars the observed distributions are noisy, but one can still see that the model slightly overpredicts the number of low mass stars. For RC stars, the models seem to significantly overpredict the number of low mass stars. This can be seen more clearly in Fig. 15 where we combine the results from all K2 campaigns to boost the sample size. The predicted distribution from the Galaxia (MP) model (as discussed in Section 4.1, the default galaxia model before the findings of Sharma et al. 2019), with its very metal poor thick disc, is also shown for comparison. Its inability to reproduce the κ_M distribution even for the lRGB stars is confirmed here with all campaigns. A more detailed quantitative comparison is given in Table 2, where we list the ratio of observed to predicted median κ_M for different K2 campaigns, which reinforce the qualitative trends discussed above. The table shows that for lRGB stars the median of the observed distribution is higher by only 2.2 per cent for K2, but it is higher by 4.1 per cent for Kepler.

Figure 15.

The distribution of κ_M for oscillating giants in Kepler and K2. Distributions for high-luminosity RGB, RC, and low luminosity RGB stars are shown separately. The shaded region denotes the 16 and 84 percentile Poisson uncertainty around the observed data. Predictions based on galaxia for the model MP (default metal- poor model from Sharma et al. 2011) and MR (improved metal-rich model from Sharma et al. 2019) are also shown in each panel.

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For RC stars, as shown in Table 2 the bias is small for Kepler (1.8 per cent) but is significant for K2 (15 per cent). The mismatch between the observed and the predicted distribution for RC stars could be due to the model being inaccurate. For example, inaccuracies in the Galactic model (or underlying stellar models) or inaccuracies in predicting the asteroseismic parameters for the modelled sample. However, given that K2 fails to measure Δν for a significant number of RC stars (Fig. 9), it is possible that low mass stars preferentially evade Δν measurement. There is some circumstantial evidence from Kepler to support this, which can be seen from Fig. 15. For Kepler, we do not have any Δν incompleteness and we also do not see any discrepancy with model predictions.

For hRGB both K2 and Kepler show differences with respect to model predictions. However, the overall number of hRGB stars is low (about 10 per cent of oscillating giants) so the statistical uncertainty in measuring the median κ_M is also higher for them. Other than inaccuracies in the model, detection completeness just like clump stars could also be an issue at least for K2. Due to problems with hRGB and RC stars, for our discussion we focus exclusively on the lRGB stars, which are the dominant population of stars in K2.

5 IMPLICATIONS FOR ASTEROSEISMIC SCALING RELATIONS AND GALACTIC ARCHAEOLOGY

In this section we will discuss the implications of our findings from the previous section on seismic scaling relations (see Hekker 2020, for a review) and on Galactic archaeology, while putting that into context of previous studies. Earlier studies indicated that asteroseismology overestimated masses, found by comparing them with the expected mass of metal poor giants in the Kepler sample (Epstein et al. 2014), and dynamical mass measurements of binary systems (Gaulme et al. 2016). Based on Stello et al. (2009), White et al. (2011), and Miglio et al. (2013), Sharma et al. (2016) showed that there are theoretically motivated corrections to the Δν scaling relation, which are important to take into account and these corrections can significantly reduce the discrepancy for metal-poor giants noticed by Epstein et al. (2014). However, the situation regarding the eclipsing binaries is more complicated. Gaulme et al. (2016) suggested 15 per cent overestimation of mass in spite of Δν corrections, while the work by Brogaard et al. (2018) suggested a good match with the dynamical masses for at least some binaries.

Population synthesis-based Galactic models, provide an indirect way to validate the asteroseismic estimates, assuming that the models are accurate. These models have been constructed independently of asteroseismology and built to satisfy a number of observations, such as photometric star counts, kinematics, and stellar abundances from spectroscopic surveys. Studies using Kepler data showed that the models predict too many low mass stars compared to the observed mass distributions, both for giants (Sharma et al. 2016) and subgiants (Sharma et al. 2017). However, doubts about the reproducibility of the complicated selection function of Kepler, prevented us from drawing any strong conclusions. This problem was alleviated by K2GAP, because of its easily reproducible selection function. Using data from four K2 campaigns, Sharma et al. (2019) showed that most of the discrepancy was due to the metallicity of the thick disc being too low in the models. For Kepler there was also improvement but some disagreement still remained.

The result of Sharma et al. (2019) is confirmed here (Section 4.6) using data from 16 K2 campaigns. Table 2 shows that for K2 lRGB giants, the mass is overestimated with respect to models by 2.2 per cent while for Kepler lRGB giants it is overestimated by 4.1 per cent. In other words, the systematics associated with masses is about 1.9 per cent lower for K2 as compared to Kepler. This is consistent with findings of Sharma et al. (2021b), who showed that kinematics can be used to estimate the age of an ensemble of stars and hence test the asteroseismic scaling relations. They concluded that the asteroseismic ages of K2 stars are correct but that of Kepler stars are underestimated by at least 10 per cent. Assuming main sequence lifetime varies with stellar mass M as M⁻³ (Kippenhahn, Weigert & Weiss 2013; Miglio et al. 2017), implies that the mass in Kepler is overestimated by about 3.6 per cent. The exact reason for the systematic difference between Kepler and K2 is not yet clear, however, it is clear that this systematic is related to the K2 light curve being significantly shorter. Zinn et al. (2022) demonstrate in their fig. 5 that Kepler data, when shortened to K2 time baselines, leads to an underestimation of ν_max by about 1 per cent (hence mass by 3 per cent), in agreement with our findings here and that of Sharma et al. (2021b). To conclude, both Kepler and K2 results (after taking the systematic due to light-curve length into account) suggest that there is a discrepancy of about 4 per cent (or 11 per cent in age) between the observed and model-predicted masses, with the observed masses being higher. We now look at possible ways to resolve the discrepancy.

An interesting possibility for systematics associated with asteroseismic mass and age is given by Warfield et al. (2021). They propose that the ages of high [α/Fe] stars are underestimated by stellar models by about 10 per cent. Traditionally, the Salaris & Cassisi (2005) formula is used to account for [α/Fe] enhancement by assuming solar composition, but increasing the metallicity. Warfield et al. (2021) suggest that this approach is not sufficient. Small change in asteroseismic scaling relation is another possibility, for example the required change in ν_max is only 1.1 per cent.

Recent results by Sharma et al. (2021a,b, 2022) point out that the thick disc model adopted by galaxia is too simplistic. These results suggest that there is no distinct thick disc, instead the whole disc is considered to be a continuous sequence of stars in age, with no natural boundary between thick and thin discs (see also Schönrich & Binney 2009; Bovy, Rix & Hogg 2012). Adopting such changes to the model can potentially improve the agreement with the observed κ_M distribution, but because they alter the age and metallicity distributions in the Galactic model, they cannot resolve the discrepancy found by Sharma et al. (2021b) with respect to kinematic ages. This suggests that it is necessary to adjust how we predict ν_max and Δν for each star in the model from the stellar mass, age, and chemical composition.

6 SUMMARY AND CONCLUSIONS

In this paper, we have provided an overview and motivation of the K2GAP Guest Observer programme, whose main aim is to study the Galaxy through asteroseismology of giants. The programme was designed to select stars with an easily reproducible selection function. A total of 110 791 targets were allocated through K2GAP, accounting for 25 per cent of the stellar targets observed by K2. Among these, 101 419 stars follow a well-defined colour–magnitude selection. One of the most important contributions of this work is providing rigorous selection function criteria for each campaign in a tabular form. A python code implementing the selection function is also provided. We also provide a catalogue of all stars observed by K2 along with flags to identify stars belonging to our programme and stars that strictly satisfy our prescribed selection criteria. In order to facilitate comparison with predictions of theoretical Galactic models, we also provide selection-matched mock catalogues generated using galaxia. We present a simple and efficient ‘change point identification’ algorithm used to screen out K2 stars that were proposed by the K2GAP but were serendipitously selected by NASA through other Guest Observer programmes.

Our work provides useful guidelines for designing future astronomy surveys. In cases where we lack decisive data to select the desired targets it is better to avoid complicating the selection criteria for a marginal increase in efficiency. We show that sometimes adopting an approach inclusive of more science cases can greatly simplify the selection function.

We show that asteroseismic giants in K2 span a wide range of R and |z| in the Galaxy, offering a significant advantage for Galactic studies compared to Kepler. K2 also contains significantly older stars than Kepler, which are useful to probe the early history of the Galaxy. However, the wider coverage comes at the price of light curves having shorter duration, and consequently lower SNR.

Some of our main results are as follows

• We estimate the detection completeness of ν_max and Δν measurements. For K2 the probability to detect ν_max was 86 per cent, which is lower but very similar to Kepler (89 per cent). However, unlike Kepler, in K2 not all stars with ν_max measurements have a Δν measurement. The probability to detect Δν is maximum at around ν_max = 60 |$\mu$|Hz and falls off for higher and lower values of ν_max. This is due to lower SNR and frequency resolution of K2 compared to Kepler.

• The probability to detect Δν shows a minimum at ν_max ∼ 30 |$\mu$|Hz as also reported by Zinn et al. (2022). This suggests that it is more difficult to detect Δν for an RC star as compared to an RGB star, most likely due to the oscillation power spectra of RC stars being more complex, in agreement with findings of Mosser et al. (2019).

• The observed to model-predicted ratio of giants with ν_max measurement is exceptionally low for C11 (0.3) suggestive of data quality issues with this campaign. The campaign has a roll angle error and has a shorter observing duration.

• The distributions of RGB and RC stars in the (ν_max, κ_M) plane show a good match with model predictions. However, some differences can also be seen. The location of the RGB-bump is at a lower ν_max in the models compared to the observations as expected from shortcomings in stellar evolution models (Silva Aguirre et al. 2020). Some RGB stars are found to be classified as RC in K2.

• We compared the observed κ_M distribution with those of model predictions for hRGB, RC, and lRGB giants. For Kepler, the distribution for all giant classes are in reasonable agreement with theoretical predictions (with medians differing by less than 5 per cent). However, for K2 only the lRGB distributions are in reasonable agreement (with medians differing by only 2.2 per cent). For the RC and the hRGB there is a mismatch and this is most likely due to significant incompleteness in Δν measurements for K2.

• The K2 masses for lRGB giants have a systematic offset of about 1.9 per cent compared to Kepler, which is in agreement with findings of Sharma et al. (2021b) based on stellar kinematics. As discussed in Zinn et al. (2022, see their fig. 5), this systematic offset is due to the shorter time baseline of K2 compared to Kepler. After correcting for this systematic, data from both K2 and Kepler suggest that asteroseismic masses of lRGB stars are higher by about 4 per cent compared to model predictions. Some of this discrepancy could be due to inaccurate modelling of [α/Fe] enhanced stars (Warfield et al. 2021), and some of it could be due inaccuracies in modelling the Galactic disc Sharma et al. (2021a,b). In future, a further improvement in both the stellar and Galactic models is required.

ACKNOWLEDGEMENTS

We would like to thank the entire community supporting the K2 GAP. SS is funded by a Senior Fellowship (University of Sydney), an ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO-3D) Research Fellowship and JBH’s Laureate Fellowship from the Australian Research Council (ARC). JBH is supported by an ARC Australian Laureate Fellowship (FL140100278) and ASTRO-3D. JCZ is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2001869. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement No. DNRF106). Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.

This publication makes use of data products from the Two Micron All Sky Survey (2MASS), which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration (NASA) and the National Science Foundation (NSF).

This paper includes data collected by the Kepler mission and the K2 mission. Funding for the Kepler mission and K2 mission are provided by the NASA Science Mission directorate.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France (DOI : 10.26093/cds/vizier). The original description of the VizieR service was published in Ochsenbein, Bauer & Marcout (2000) This research made use of the following software: Python 3, numpy (Harris et al. 2020), matplotlib (Hunter 2007).

DATA AVAILABILITY

The data sets used are available for download at http://www.physics.usyd.edu.au/k2gap/download. There is a master catalogue of all observed K2 targets. There is another catalogue that contains both observed and simulated targets following the selection function described in Table 1, see Appendix  C for further details. The python code for selection function is available at https://github.com/sanjibs/k2gap.

Footnotes

REFERENCES

APPENDIX A: THE 2MASS QUALITY SELECTION CRITERIA

K2GAP stars were selected from the all sky 2MASS catalogue. The 2MASS quality flags were used to select stars with good quality photometry and the criteria used is given below in Table A1. For further details on flags see 2MASS documentation at https://vizier.u-strasbg.fr/viz-bin/VizieR.

APPENDIX B: PRIORITY CLASSES OF PROPOSED TARGETS

In the K2 guest observer programme, each team was asked to submit a ranked list of proposed targets. Separate target lists were created for each campaign. To prepare the target list we began by assigning targets to various priority classes. Next, we sorted the targets based on priority classes and then for targets in each class we further sorted them in increasing order of magnitude. Below we describe the different priority classes that were used by us.

Classes with order less than 10 were for stars known to be giants from either spectroscopy or asteroseismology or were special targets. We included stars with existing spectroscopy from surveys such as APOGEE, RAVE, GAIA-ESO, and SEGUE. From previous experience with Kepler, it was known that seismic detections were possible for 1.9 < log g < 3.5. Given spectroscopic log g have uncertainties of the order of 0.1 dex, a criterion of log g < 3.8 was adopted for the spectroscopic sample. A lower limit on log g was not adopted as there are very few stars with log g < 1.9.

APPENDIX C: CATALOGUE OF TARGETS

As part of this paper we provide a couple of useful catalogues, which are available for download, for details see the section on data availability. First is a master catalogue of all targets observed by K2 and it is in file k2_observed_targets.fits. To construct this catalogue we start with a list of epic_ids of observed targets from the Kepler science website.⁴ It also contains campaign names campaign, which we convert to an integer cno. This list includes all targets selected by any of the K2 programmes, not just those proposed by the K2GAP. We first cross-matched it to the epic catalogue based on epic_id and added columns from it. To supplement the photometric information from 2MASS, we did our own cross match with 2MASS instead of relying on the information provided by the EPIC catalogue (Huber et al. 2016). This was because the EPIC catalogue was missing entries for about 13 000 targets, in spite of targets being stars (⁠|$\tt {epic\_id} \gt 201000000$|⁠). Moreover, the 2MASS columns mflg and prox were incorrect for the majority of the stars in the EPIC. These flags, among others, were used in K2GAP to select stars with good quality photometry (Table A1). The catalogue contains 588 991 targets. For the rest of the paper we exclusively focus on the 432 830 targets that have epic_id > 201000000; the rest being non-stellar targets like asteroids, planets, moons, and so on. To the base catalogue we have added two additional columns that provide information about the K2GAP (flag_ga and flag_sf). Targets that are on the K2GAP target list have flag_ga = 1 of which there are 132 197 in total. This amounts to 30.5 per cent of all the observed K2 targets. These stars also include the ‘serendipitous’ ones selected by other programmes that are in the K2GAP target list. We remove the serendipitous targets to create a K2GAP-chosen sample (referred to as K2GAP complete), following a procedure that is described in Section 2.4. A majority of the K2GAP complete targets follow a strict colour magnitude selection function (101419), and these can be identified with flag_sf = 1.

The second catalogue that we provide is that of targets that follow a clean reproducible selection function as described in Table 1 and this is in file k2_observed_targets.fits. This contains both observed targets as well as selection function matched targets simulated by galaxia. This should be useful for studies related to Galactic archaeology.